Parametrization of the Cosmic Muon Flux for the Generator CMSCGEN

The cosmic muon generator CMSCGEN is based on a parametrization of the differential muon flux at ground level, as obtained from the air shower simulation program CORSIKA. We present the underlying ansatz for this parameterization and provide an approximation of the momentum and angular distributions in terms of simple polynomials, in the momentum range 3 to 3000 GeV.

💡 Research Summary

The paper presents a practical and accurate parametrization of the differential cosmic‑muon flux at sea level for use in the CMSCGEN muon generator. The authors start by generating a large reference dataset with the air‑shower simulation program CORSIKA (version 6.720). Primary cosmic‑ray particles (protons and helium nuclei) are injected at the top of the atmosphere following a power‑law energy spectrum (E‑2.7) and a uniform distribution of incident angles. The simulation adopts the US‑Standard 1976 atmospheric model, a fixed geographic location (latitude ≈ 46°, longitude ≈ 6°, i.e., near CERN), and records all muons that reach ground level. The resulting muon sample covers a momentum range from 3 GeV to 3000 GeV and zenith angles from 0° to 90°, providing a dense two‑dimensional (p, θ) histogram with well‑controlled statistical uncertainties.

To convert this detailed simulation output into a compact analytical form, the authors adopt an ansatz that combines a basic power‑law dependence in momentum with an angular factor, multiplied by low‑order polynomial corrections. The functional form is:

 Φ(p, θ) = A · p^‑γ · (1 + cos θ)^β ·